Soft corrugated channel with synergistic exclusive discrimination gating for CO2 recognition in gas mixture

Developing artificial porous systems with high molecular recognition performance is critical but very challenging to achieve selective uptake of a particular component from a mixture of many similar species, regardless of the size and affinity of these competing species. A porous platform that integrates multiple recognition mechanisms working cooperatively for highly efficient guest identification is desired. Here, we designed a flexible porous coordination polymer (PCP) and realised a corrugated channel system that cooperatively responds to only target gas molecules by taking advantage of its stereochemical shape, location of binding sites, and structural softness. The binding sites and structural deformation act synergistically, exhibiting exclusive discrimination gating (EDG) effect for selective gate-opening adsorption of CO2 over nine similar gas molecules, including N2, CH4, CO, O2, H2, Ar, C2H6, and even higher-affinity gases such as C2H2 and C2H4. Combining in-situ crystallographic experiments with theoretical studies, it is clear that this unparalleled ability to decipher the CO2 molecule is achieved through the coordination of framework dynamics, guest diffusion, and interaction energetics. Furthermore, the gas co-adsorption and breakthrough separation performance render the obtained PCP an efficient adsorbent for CO2 capture from various gas mixtures.

and supported by additional computational investigations. Congratulations! While I mostly agree with the interpretation and discussion provided I think that particularly the computational investigation does not live up to the level of the experimental investigations. As such there are a few comments which I would like the authors to address with an otherwise great paper that should be published in Nature Comms.
The single component adsorption isotherms were recorded at the standard boiling points of the respective gases. Many of the conditions are quite unusual for adsorption investigations. I recognize that similar temperature ranges have been investigated by Kaskel and co-workers in this paper: https://pubs.rsc.org/en/content/articlelanding/2021/fd/d0fd00013b Is this temperature selected to record the full relative pressure range up to 100 kPa or is the reasoning different? Can the authors detail to why these conditions were chosen and how they might influence the described selectivity?
A long standing question in the field of soft porous crystals with respect to selective adsorption is the co-adsorption of various guest species after pore-opening has occurred. The authors describe the size-selective adsorption sites for CO2 and hydrocarbons but did not discuss the (quasi)equilibrium situation of co-adsorption after pore opening in details. There is only a very short section that details experiments which are otherwise "hidden" in the ESI. I suggest to comment on this aspect a bit more in detail. For example if the CO2 is blocking the pore entry and prevents effective exchange in the pore network etc.
In the main text and ESI the phrase "exposure time" correlates to the equilibration time of individual adsorption steps? A clarification might be helpful given that the authors not only record isotherms but also isobars.
I suggest to add a schematic energy diagram in Figure 5 (similar to figure 4) that supports and summarizes the evolution of the energy landscape in this system.
In the computational analysis the authors describe by DFT the evolution of binding energies vs loading of various adsorption sites. Did the authors consider the contribution of CO2-CO2 (or more general gas-gas) interactions in these calculations and can they derive to what extend these interactions contribute the less favorable adsorption energetics with enhanced loading? The authors state: "These results indicate that the selective adsorption of CO2 over C2H2 and C2H4 was not thermodynamically but kinetically controlled." In the simulations only single gas scenarios have been computed and although I agree that the data of this work indicates this scenario the computation is the weakest link in this regard. Maybe it would be helpful to refer to the experimental data or draw a detailed comparison.
The authors use the climbing-image nudged elastic band (CI-NEB) method to evaluate the diffusion barrier. However, in this model the framework is treated as a rigid entity which based on the experimental finding is certainly not the case in this system. In addition, this approach provides no insight into the co-diffusion in gas mixtures in which CO2 may allow to open the pore structure allowing other gases to enter as well. I am thus skeptical to what degree these calculations are an adequate description of the real world scenario and in fact to what degree they can contribute to establish the underlying mechanism. Did the authors try to apply molecular dynamics simulations in this system as this is an established method to reliably determine diffusion processes as well as structural deformations in PCPs and other dynamic porous solids. 1. A few references have reported highly selective adsorption of CO2 over hydrocarbons or over inorganic gases. It is better to compare the results with the known examples, including performances and mechanisms. 2. Fig. 1d is claimed as synergistically utilizing all available recognition mechanisms as shown in Fig. 1a-c. However, the concept in Fig.1a is not involved in Fig. 1d. For the computational simulation of the diffusion barrier, the dyanmism or the transient structural distortion of the narrow window is considered, which is consistent with the concept shown in Fig. 1d. Therefore, it is suggested to revise Fig. 1a according to the that of Fig.1d and the computational simulations. 3. Are the two large circular pores in Fig. 1d represent rigid or soft? If rigid, it is not the case for the titled PCP. If soft, the structural transformation is not shown. 4. The term Exclusive Discrimination seems to refer to an ideal selectivity. However, as the manuscript stated, many of the 9 gases can be adsorbed. In the literature, thermodyanmic separation would not be stated as exclusive/ideal even when the selectivity is extremely high. It would be better to revise or clarity the term. 5. The orientation of Fig 2a is not suitable to reveal the structural relationship with that in Fig. 2b. Please describe how many Co(II) ions are coordinated to the 3,5-pdc2-and dpg ligands, in all three phases. It is suggested to draw the simplified topological structures of the three phases. 6. As shown in Fig. 2d-e, the uptake below the gate-opening pressure is attributed to the inclusion of CO2 in the intrinsic microporous cavities of phase beta. However, phase beta is claimed as dense in other places. Please clearly compare the crystallographic pore parameters (in a table) and the pore structures (in a figure) of the three phases. Before doing these, please polish the crystal structures to eliminate the errors such as A/B-level alerts, missing hydrogen atoms, nonplanar aromatic rings, etc. 7. About the Hill coefficient, reference should be cited, and the discussion seems to be too simple and meaningless. 8. …CO2 required activation energy to adsorb onto… What's the meaning of activation energy? …such adsorption did not occur… Which is "such adsorption"? 9. Specify the pressure of isobars. Specify the phase used for computational simulations. 10. The volume of N2, CH4, and C2H4 adsorbed in the binary adsorption mixtures was negligible. They should not be claimed as negligible. If negligible, the uptakes should not be compared and calculated. … optimum selectivity… How optimum? This is a typical feature of gate-opening adsorption. What is "this"?

Response to the reviewer comments
Journal Name：Nature communications Manuscript Title: Soft Corrugated Channel with Synergistic Exclusive Discrimination Gating for CO2 Recognition in Multicomponent Gas Mixture Manuscript No: NCOMMS-23-07080-T Thank the referees for their helpful comments and suggestions. Based on these comments and suggestions, related changes have been done in the revised manuscript as follows: Reviewer #1: In this paper, authors prepared a novel MOF PCP-3,5-pdc and this MOF exhibited unprecedented selectivity to carbon dioxide over various gas molecules in high pressure through extraordinary gate-opening phenomenon via phase transition of MOF. The unique affinity of CO2 was confirmed by the mixture gas co-sorption experiment, high-pressure sorption, and high-pressure breakthrough. Furthermore, the underlying mechanism of this phase-transition-based gate-opening behavior of PCP-3,5-pdc was successfully rationalized by gas-loaded Rietveld refinement, DFT calculation, and energy barrier calculation. And the additional adsorption isotherms which vary the exposure time further underpinned the author's claim that kinetic factor matter when it comes to differentiating similar molecules such as acetylene and ethylene. I believe that this research has a significant impact because selectively capturing carbon dioxide is crucial for applications including carbon capture, purifying hydrocarbon, and so on. Moreover, this kind of gate-opening due to the guest molecule in the high-pressure region is barely reported Last but not least, I believe that the gateopening phenomenon presented in this paper has much potential in terms of practical application compared to gate-opening occurring under 1 bar since conventionally highpressure gas or compressed gas were used in the practical application field. However, the experimental detail or explanation of high-pressure techniques (cosorption experiments, high-pressure sorption, and breakthrough experiments) was not sufficient. (Especially, in the case of high-pressure isotherm there were any explanations at all except for the acknowledgment section) And given that standardized protocols and procedures for high-pressure experiments were not constructed yet among the researchers and the fact that the result of high-pressure experiments has a high chance of being affected by a systematic error, I believe throughout the explanation of experimental detail of high-pressure experiments were mandatory. To sum up, I would like to recommend this paper to be published after the author reflect on the following recommendation.

Response
We are grateful to the reviewer for their time and effort in evaluating our manuscript and recognizing its "significant impact". We really appreciate the reviewer's constructive comments to improve the quality of our manuscript. We have carefully considered the remarks mentioned by the reviewer and have made the relevant revisions to the manuscript. Notably, we have added an explanation of the high-pressure experiments.
1. Author must add the experimental detail of high-pressure co-sorption experiments, high-pressure sorption measurements, and high-pressure breakthrough respectively.

Response
We thank the reviewer for this comment. We have included the experimental detail of high-pressure co-sorption experiments, high-pressure sorption measurements, and high-pressure breakthrough experiments. The relevant information is outlined below.

High-pressure Sorption Experiments (Page S3 and S22)
High-pressure sorption experiments were carried out by the volumetric BELSORP HP (MicrotracBEL Corp.) instrument (Flow diagram is shown in Supplementary Figure  12). Prior to the measurement, the blank sample cell weight was measured. The sample was then loaded into the sample cell and heated to 373 K for activation, after which the the pretreated sample was weighted. The adsorption measurement method was the volumetric method, wherein the volume of measurement system was precisely determined to calculate the volume of adsorption. Then, the volume of adsorption was calculated from the gas pressure change in the measurement system using the gas equation. The dead volume of the sample cell was measured using helium gas of 99.9999% purity. Non-ideal corrections were made by applying virial coefficients at respective measurement temperatures.

High-pressure Co-sorption Experiments (Page S3 and S26)
High-pressure co-sorption experiments were carried out by the volumetric BELSORP VC (MicrotracBEL Corp.) instrument connected to an Agilent 490 Micro gas chromatographic (GC) system equipped with a thermal conductivity detector (TCD). The flow diagram in Supplementary Figure 16a 1 provides a visual representation of the experimental setup. In a typical experiment, the sample was first loaded into a pre-weighed stainless-steel sample tube, and activated under dynamic vacuum at 373 K overnight. After activation, the exact sample weight was determined. Then, the sample tube was connected with the instrument and sealed with a metal gasket. Prior to the measurements, the samples were re-heated to 373 K for activation through removeable heater. During measurements, the temperature of the sample was set to be 298 K using a removable temperature control unit. Ultra-high purity helium gas (99.9999%) was used to measure the dead volume of the sample tube. The measurement principle is depicted shown in Supplementary Figure 16b Figure 16f). After a certain equilibration time, the total amount of adsorbed gas is calculated using a constant volume method, and the composition ratio of the adsorbed gas mixture is analyzed using GC. The non-adsorbed gas phase over the sample is used to estimate the ratio of the adsorbed gas (Supplementary Figure 16g). Based on this data, the adsorbed amounts and partial pressures of each gas were calculated.

Breakthrough Experiments (Page S4 and S27)
The breakthrough experiments were carried out using a custom-build dynamic mixed-gas breakthrough setup (Supplementary Figure 17). In a typical experiment, 1 g of PCP-3,5-pdc sample was packed into a stainless-steel column with inner dimensions of ϕ = 8 mm. The mixed-gas flow and pressure were controlled by using pressure-control valves (Swagelok) and mass flow controllers (Brooks instrument). Outlet effluent from the column was continuously monitored using a quadrupole-type mass spectrometer, BEL Mass (MicrotracBEL Corp.). The column packed with powder sample was first purged with a flow of He (20 mL·min -1 ) for 1 h at room temperature. The mixed-gas flow rate during the breakthrough process is 6 mL·min -1 using 50/50 (v/v) CO2/other gas at room temperatures. The total pressure of mixture gases was 20 bar. After the breakthrough experiment, the sample was regenerated under vacuum 24 hours for cycling measurement.
Supplementary Figure 17. The high-pressure breakthrough system used in this study.
2. The explanation or reference of co-sorption measurements by BEL-VC is required. I don't get how it differentiates the amount of adsorption in the mixed gas state.

Response
We thank the reviewer for this comment. The detailed explanation of the co-sorption measurement can be found in our response above.
3. The explanation and implication of Hill analysis ( Figure S7, S11) are needed.

Response
We thank the reviewer for this comment. We have added an explanation and implication of Hill analysis in the Supplementary Information (Page S4) as follows.
The Hill coefficient, n, is recognized as an indicator of cooperative interactions because it describes the number of molecules bound per receptor 2, 3 . The Hill coefficient is the slope of the Hill plot {log [Y/(1−Y)] versus log P}, where Y-axis is the CO2 fractional unloading and P is the gas pressure 4, 5 . Generally, n < 1 corresponds to negatively cooperative systems, while n > 1 corresponds to positively cooperative systems. To evaluate the degree of cooperativity for the gate-opening step in CO2 adsorption, we applied Hill's model analysis to the CO2 adsorption isotherm at 195 K and 298 K.
The Hill coefficient for the gate-opening step in the CO2 adsorption isotherm at 195 K was determined to be 4.1 (>1) (Supplementary Figure 9), confirming the positive, cooperative adsorption phenomenon. The positive CO2 adsorption cooperativity in the structural transformation step was even stronger (Hill coefficient n = 6.6, Supplementary Figure 14). The difference in cooperativity at different temperature may be due to the varying diffusion and stabilizing abilities of the CO2 molecules. 4. The additional explanation of separation factor calculation through co-adsorption isotherm (Figure 3d) is required. And comparison with other references is also recommended.

Response
We thank the reviewer for this comment. The separation factor is calculated based on the mixture gases co-adsorption results. The separation factor (S) is defined as: where X1 and X2 are the concentration of gas 1 and 2 in the adsorbed phase and Y1 and Y2 are the concentration of gas 1 and 2 in the feed phase. This information is provided in the Supplementary Information (Page S4).
We also thank the reviewers for suggesting comparison with other references. Usually, IAST selectivity, which is based on the ideal adsorbed solution theory, is commonly used to evaluate the potential of MOFs for capturing CO2 from gas mixtures. However, this method relies on adsorption in a solution phase, or at temperature near the boiling point of the gases being adsorbed, and is usually calculated from a singlecomponent adsorption isotherm. As a result, it may not fully represent MOF selectivity in gas separation scenarios, especially those involving structural flexibility 6,7 . In this study, we have calculated the separation factor based on the results of co-adsorption experiments with gas mixtures. This approach differs from the commonly used IAST selectivity index and is difficult to compare directly. To contextualize our results, we have compared them with other references that primarily focused on general CO2 capture performances and separation mechanisms (Supplementary Table 8 The cooperation of pore stereochemical shape, location of binding sites, and framework flexibility 5. The authors state that "Moreover, after the high-pressure adsorption test~~and natural gas processing (up to 50 bar).". Therefore, it would be better to add the references related to the high-pressure application which the authors mentioned.

Response
We thank the reviewer for this comment. As per the reviewer's advice, we have included the following references relevant to the high-pressure application: • Qazvini et al conducted the breakthrough simulations at pressures relevant to natural gas processing (50 bar) and predict that MUF-16 could capture CO2 from natural gas. This work was reported in Nature Commununications in 2021 (DOI: 10.1038/s41467-020-20489-2). We have added these references to the revised manuscript (page 11).
6. In the case of a breakthrough, they only conducted CO2/CH4 and CO2/N2 measurements. As they claimed that PCP-3,5-pdc could separate CO2 from similar gas molecules, breakthrough experiments much more relevant to there's opinion, such as CO2/C2H2, and CO2/C2H4 breakthrough experiments were required.

Response
We appreciate the reviewer's comment. Conducting the breakthrough experiments with C2H2 is not feasible because we need to perform the experiment under high pressure, and it would reach the explosive limit of C2H2 gas. In response to the reviewer's suggestion, we further performed CO2/C2H4 breakthrough experiments as shown in Supplementary Figure 21 (page 32 in the Supplementary Information), which also support the CO2 preference over C2H4 under the given condition.
Supplementary Figure 21. Experimental breakthrough curve of PCP-3,5-pdc at a flow rate of 6 mL/min for an equimolar gaseous mixture of C2H4 and CO2 (v/v, 50/50) at room temperature (Total pressure 20 bar). Figures S18, 19, and 20, It seems like the presence of vapor did not affect the structure of PCP-3,5-pdc. However, the effect of humidity in terms of separation performance is not proved. Since structure collapse and the diminution of capturing or separation performance in humid condition were big issue in the CO2 adsorption field, additional experiments that can prove the effect of humidity is recommended. (For example, humid condition breakthrough or co-sorption between vapor and CO2 and so on…)

Response
We are grateful to the reviewer for providing constructive feedback. At high-pressure conditions, the condensation of water vapor may occur. Therefore, due to the highpressure conditions required for our breakthrough or co-sorption experiments, it was not possible to perform the experiment in a humid environment. Instead, we investigated the impact of humidity on the separation performance by comparing the CO2/N2 breakthrough curves of the sample exposed to humid air for more than one week, both before and after thermal activation. Supplementary Figure S25 (Page S35) illustrates the CO2/N2 breakthrough curves of the sample, before and after activation (at 373 K under vacuum for 2 hours). The results indicate that while the CO2/N2 separation ability was sustained, its performance degraded due to humidity. However, since the structure remained stable even under humid conditions, the separation performance was not affected after activation (page 12 in the revised manuscript).
Supplementary Figure 25. Experimental breakthrough curve of PCP-3,5-pdc before and after activation (at 373 K under vacuum for 2 hours), after exposure to humidity for more than one week at a flow rate of 6 mL/min for an equimolar gaseous mixture of N2 and CO2 (v/v, 50/50) at room temperature (Total pressure 20 bar).

Reviewer #2: In "Soft Corrugated Channel with Synergistic Exclusive Discrimination
Gating for CO2 Recognition in Multicomponent Gas Mixture" Gu et al. describe the exclusive discrimination gating (EDG) effect in a porous coordination polymer (PCP) for selective CO2 adsorption over a wide range of other gases. The work strongly builds on a legacy of similar dynamic effects in porous solids by the group but still provides novel and intriguing insights. I find the manuscript well-structured and illustrated, the experimental details and volume of the data presented and discussed is extensive and supported by additional computational investigations. Congratulations! While I mostly agree with the interpretation and discussion provided. I think that particularly the computational investigation does not live up to the level of the experimental investigations. As such there are a few comments which I would like the authors to address with an otherwise great paper that should be published in Nature Comms.

Response
We thank the reviewer for reviewing our manuscript and recognizing it as "a great paper". We really appreciate the constructive comments that helped to improve the quality of our manuscript. We carefully considered all the remarks mentioned and made related revisions to the manuscript.
1. The single component adsorption isotherms were recorded at the standard boiling points of the respective gases. Many of the conditions are quite unusual for adsorption investigations. I recognize that similar temperature ranges have been investigated by Kaskel and co-workers in this paper: https://pubs.rsc.org/en/content/articlelanding/2021/fd/d0fd00013b. Is this temperature selected to record the full relative pressure range up to 100 kPa or is the reasoning different? Can the authors detail to why these conditions were chosen and how they might influence the described selectivity?

Response
We thank the reviewer for this comment. In this work, we first measured the single component adsorption isotherms at their respective standard boiling points, up to 100 kPa (Fig. 2d, page 7 in the revised manuscript). A lower temperature provides stronger host-guest interactions from thermodynamic perspective. Therefore, the single component adsorption isotherms at the standard boiling points of each gas were recorded over the pressure range up to 100 kPa to examine the gas-dependent sorption behavior of PCP-3,5-pdc. In addition, we also recorded the single-component adsorption isotherms for each gas at the same temperature of 298 K, up to 30 bar (Supplementary Figure 13, page S23). These results confirmed that, except CO2, none of the other gases induced the gate-opening behavior of PCP-3,5-pdc. This unique sorption behavior is unprecedented and therefore, interesting. This unique sorption behavior is unprecedented and, therefore, we believe it is interesting.

2.
A long-standing question in the field of soft porous crystals with respect to selective adsorption is the co-adsorption of various guest species after pore-opening has occurred.
The authors describe the size-selective adsorption sites for CO2 and hydrocarbons but did not discuss the (quasi)equilibrium situation of co-adsorption after pore opening in details. There is only a very short section that details experiment which are otherwise "hidden" in the ESI. I suggest to comment on this aspect a bit more in detail. For example, if the CO2 is blocking the pore entry and prevents effective exchange in the pore network etc.

Response
We thank the reviewer for this comment. The co-adsorption of various guest species in soft porous crystals depends on their affinities to the framework, even after poreopening has occurred. In the case of co-adsorption of CO2 and C2H4 in PCP-3,5-pdc, C2H4 is more adsorbed at room temperature than CO2 before the opening of pores. As pressure increases, the pores in this PCP can be opened by CO2 adsorption. However, the adsorption of C2H4 did not increase compared to that before the pore opening, suggesting that guest exchange is difficult to occur (Fig. 3c, page 10 in the revised manuscript). These co-adsorption results suggest that PCP-3,5-pdc has a stronger affinity for C2H4 than for CO2 before the pore-opening occurs, but a weaker affinity for C2H4 than for CO2 after the pore-opening has occurred. This is consistent with the calculated binding energies of these gas molecules with this PCP at different poreopening states. In this regard, we agree with the reviewer's suggestion to discuss further and have added a sentence in page 11 of the revised manuscript: "These results suggest that the adsorption of CO2 in the open framework of PCP-3,5-pdc is strong enough to block the pore entry, preventing effective guest exchange in the pore network.".
3. In the main text and ESI the phrase "exposure time" correlates to the equilibration time of individual adsorption steps? A clarification might be helpful given that the authors not only record isotherms but also isobars.

Response
We thank the reviewer for this comment. The exposure time is correlates to the equilibration time. We have used exposure time throughout the main text and Supplementary Information in this revised version. Figure 5 (similar to figure 4) that supports and summarizes the evolution of the energy landscape in this system.

Response
We thank the reviewer for this suggestion. We have added a schematic energy diagram in the revised Figure 5. The revised Figure 5 is shown as follows (Page 16 in the revised manuscript). We considered a diffusion process in which gas molecules moves from site I to its neighbouring site II. Interaction energies (Eint), deformation energies (Edef), and diffusion barriers (Eb) are given in kcal mol -1 .

5.
In the computational analysis the authors describe by DFT the evolution of binding energies vs loading of various adsorption sites. Did the authors consider the contribution of CO2-CO2 (or more general gas-gas) interactions in these calculations and can they derive to what extend these interactions contribute the less favorable adsorption energetics with enhanced loading?

Response
We thank the reviewer for this comment. Gas-gas interactions were considered in our DFT calculations. As shown in Supplementary Table 7 (Page S44), the gas-gas interactions (Eint, G-G) becomes more negative with enhanced CO2 loading, which is favorable for CO2 adsorption. However, as the number of CO2 molecules per unit cell increases to 4, the Eint, H-G becomes less negative, which is unfavorable for further CO2 adsorption. We revised the corresponding discussion in page 15 as follows: The increase in BE arises from the formation of T-shaped molecular clusters of CO2 between the adsorbed CO2 molecules stabilizing gas-gas interactions, which stabilizes gas-gas interactions, and the decrease in average deformation energy of PCP induced by CO2 adsorptions (Fig. 4a and Supplementary Table 7). However, the BE value decreases (less negative) when four CO2 molecules are adsorbed at all the adsorption sites II to afford PCP•4CO2 (Fig. 4c) because of the congestion due to the 'narrowcorrugated channel', as suggested by the decreased interaction energy (Eint, H-G) between CO2 molecules and PCP framework (Supplementary Table 7).
6. The authors' state: "These results indicate that the selective adsorption of CO2 over C2H2 and C2H4 was not thermodynamically but kinetically controlled." In the simulations only single gas scenarios have been computed and although I agree that the data of this work indicates this scenario the computation is the weakest link in this regard. Maybe it would be helpful to refer to the experimental data or draw a detailed comparison.

Response
We thank the reviewer for this comment and agree with this reviewer that our original statement might be too strong without referring to experimental data. According to the calculated binding energy, PCP-3,5-pdc has a stronger affinity to C2H2 or C2H4 than to CO2. Therefore, this PCP can should selectively adsorb C2H2 or C2H4 over CO2, which is not observed at low temperature. Actually, experimental results of high-pressure gas adsorption at room temperature also support that PCP-3,5-pdc has a stronger affinity to C2H2 or C2H4 than to CO2. Therefore, we inferred that kinetic factors may play important roles for the selective adsorption of CO2 over C2H2 and C2H4, which were discussed in the subsequent section by referring to both computational and experimental data. Therefore, we revised the sentence as "These results suggest that the selective adsorption of CO2 over C2H2 and C2H4 at low temperature was not thermodynamically but could be kinetically controlled, as discussed below." for clarity (Page 17 in the revised manuscript). 7. The authors use the climbing-image nudged elastic band (CI-NEB) method to evaluate the diffusion barrier. However, in this model the framework is treated as a rigid entity which based on the experimental finding is certainly not the case in this system. In addition, this approach provides no insight into the co-diffusion in gas mixtures in which CO2 may allow to open the pore structure allowing other gases to enter as well. I am thus skeptical to what degree these calculations are an adequate description of the real world scenario and in fact to what degree they can contribute to establish the underlying mechanism. Did the authors try to apply molecular dynamics simulations in this system as this is an established method to reliably determine diffusion processes as well as structural deformations in PCPs and other dynamic porous solids.

Response
We thank the reviewer for this comment. As pointed out by this reviewer, co-adsorption and co-diffusion of gas mixtures are open questions in the field of soft porous crystals. It is still unclear whether the pore opened by adsorption of one gas molecule can keep open permanently and allow adsorption/diffusion of other gas species. To fully address this question, a comprehensive computational study on the equilibrium and nonequilibrium adsorptions using various computational methods is required, as recommended by this reviewer. However, to our understanding, this is a bit beyond the scope of this work. In the present work, gas molecules are adsorbed in the onedimensional narrow-corrugated channels of PCP-3,5-pdc, which only allows gas adsorption/diffusion in a sequential manner. In addition, the co-adsorption experiment suggest that the pores opened by CO2 adsorption rarely allow the entry of other gas species. Besides, both room-temperature gas adsorption measurement and DFT calculations on equilibrium gas adsorption suggest that PCP-3,5-pdc should have a stronger affinity to C2H4 than to CO2 before pore-opening has occurred. However, at low temperatures near to the boiling points of gas molecules, the adsorption amount of CO2 is larger than that of C2H4 even before pore-opening has occurred. Therefore, we inferred that calculating the diffusion barriers of various gas molecules could give insight into their different adsorption behaviors. In this regard, we think the CI-NEB method is useful to calculate the diffusion barriers of gas molecules before poreopening has occurred, which leads to reasonable values to understand the difference in adsorption behavior between CO2 and hydrocarbons. Given above considerations, we did not try to apply molecular dynamics simulations in this work but will keep in mind while trying to theoretically address the open question of co-adsorption and codiffusion of gas mixtures in selected soft porous crystals.
Reviewer #3: Prof. Kitagawa and coworkers reported a flexible PCP showing highly selective CO2 adsorption over 9 typical gases, which has not been achieved by other materials. While most references still focus on separation of simple/ideal mixtures containing two or three components, this result would call attention for separation of highly complicated mixtures. I strongly suggest publication of this work with some minor concerns.

Response
Thanks to the reviewer for reviewing our manuscript and strongly recommending the publication of this work. We really appreciate the constructive comments that helped to improve the quality of our manuscript. We carefully considered all the remarks mentioned and made related revisions to the manuscript.
1. A few references have reported highly selective adsorption of CO2 over hydrocarbons or over inorganic gases. It is better to compare the results with the known examples, including performances and mechanisms.

Response
We thank the reviewer for this comment. Herein, we added a comparison with other reference mainly focused on general CO2 capture performances and separation mechanisms (Supplementary Table 8, page S53). This table can be found in our response to Reviewer #1's comment 4.
2. Fig. 1d is claimed as synergistically utilizing all available recognition mechanisms as shown in Fig. 1a-c. However, the concept in Fig.1a is not involved in Fig. 1d. For the computational simulation of the diffusion barrier, the dynamism or the transient structural distortion of the narrow window is considered, which is consistent with the concept shown in Fig. 1d. Therefore, it is suggested to revise Fig. 1a according to the that of Fig.1d and the computational simulations.

Response
We thank the reviewer for this comment. We revised the Fig. 1a according to the reviewer's suggestions. The revised Fig. 1a shows the molecular sieving and diffusion regulation mechanisms in rigid PCPs. In the Fig. 1d, the bottleneck aperture in the corrugated channel after gate-opening also can show molecular sieving and diffusion regulation functions. The revised Fig. 1a is shown as follows (Page 5 in the revised manuscript).
3. Are the two large circular pores in Fig. 1d represent rigid or soft? If rigid, it is not the case for the titled PCP. If soft, the structural transformation is not shown.

Response
We thank the reviewer for this comment. We have included the structural transformation in the revised Fig. 1d, which is displayed below.
4. The term Exclusive Discrimination seems to refer to an ideal selectivity. However, as the manuscript stated, many of the 9 gases can be adsorbed. In the literature, thermodynamic separation would not be stated as exclusive/ideal even when the selectivity is extremely high. It would be better to revise or clarity the term.

Response
We thank the reviewer for this comment. In this revised manuscript, we use the term exclusive discrimination gating effect to refer to the selective gate-opening adsorption behavior for CO2 over other 9 gases. We clarify the term in the revised manuscript (page 2 in the revised manuscript). Fig 2a is not suitable to reveal the structural relationship with that in Fig. 2b. Please describe how many Co(II) ions are coordinated to the 3,5-pdc-and dpg ligands, in all three phases. It is suggested to draw the simplified topological structures of the three phases.

Response
We thank the reviewer for this comment. The following Supplementary Figure 3a-c show the coordination environment of Co(II) in as-synthesised, activated and CO2 loaded PCP-3,5-pdc. In the as-synthesised PCP-3,5-pdc, each Co(II) is coordinated to three 3,5-pdc and three dpg ligands. In the activated and CO2 loaded PCP-3,5-pdc, each Co(II) is coordinated to three 3,5-pdc and two dpg ligands. As per the reviewer's advice, the simplified topological structures of the three phases have been added to page S12 in the revised Supplementary Information (Supplementary Figure 3d-f).
Supplementary Figure 3. (a-c) The coordination environment of Co(II) in phase α, β and γ of PCP-3,5-pdc. (d-f) The simplified topological structures of phase α, β and γ of PCP-3,5-pdc. In the as-synthesised PCP-3,5-pdc, each Co(II) is coordinated to three 3,5-pdc and three dpg ligands. In the activated and CO2 loaded PCP-3,5-pdc, each Co(II) is coordinated to three 3,5-pdc and two dpg ligands. Fig. 2d-e, the uptake below the gate-opening pressure is attributed to the inclusion of CO2 in the intrinsic microporous cavities of phase beta. However, phase beta is claimed as dense in other places. Please clearly compare the crystallographic pore parameters (in a table) and the pore structures (in a figure) of the three phases. Before doing these, please polish the crystal structures to eliminate the errors such as A/B-level alerts, missing hydrogen atoms, nonplanar aromatic rings, etc.

Response
We thank the reviewer for this comment. As per the reviewer suggestion, we polished the crystal structures while taking care of the A/B-level alerts (the updated results are summarized in Supplementary Table S2, and S3). Regarding the Rietveld analysis result of the CO2 adsorbed phase (γ), the nonplanar aromatic rings and the missing hysrogen atoms resulted because this structural analysis was performed based on the PXRD pattern analysis without using a rigid-body model (the refinement detail is given in Supplementary Information Page S5, and Supplementary Table S5). Therefore, prior to the structural comparisons of these structure, we computationally optimzed the γ structure by adding the hydrogen atoms with keeping the same unit cell parameter and fixing metal position. As per the reviwer's helpful suggestion, we have included the voids ratio and pore structures in the revised Supplementary Information (page S18) as shown below.
Supplementary 7. About the Hill coefficient, reference should be cited, and the discussion seems to be too simple and meaningless.

Response
We thank the reviewer for this comment. We have added the explanation and implication of Hill analysis in the Supplementary Information (Page S4-5) as follows. The Hill coefficient, n, is recognized as an indicator of cooperative interactions because it describes the number of molecules bound per receptor 2, 3 . The Hill coefficient is the slope of the Hill plot {log [Y/(1−Y)] versus log P}, where Y-axis is the CO2 fractional unloading and P is the gas pressure 4, 5 . Generally, n < 1 corresponds to negatively cooperative systems, while n > 1 corresponds to positively cooperative systems. To evaluate the degree of cooperativity for the gate-opening step in CO2 adsorption, we applied Hill's model analysis to the CO2 adsorption isotherm at 195 K and 298 K.
The Hill coefficient for the gate-opening step in the CO2 adsorption isotherm at 195 K was determined to be 4.1 (>1) (Supplementary Figure 9), confirming the positive, cooperative adsorption phenomenon. The positive CO2 adsorption cooperativity in the structural transformation step was even stronger (Hill coefficient n = 6.6, Supplementary Figure 14). The difference in cooperativity at different temperature may be due to the varying diffusion and stabilizing abilities of the CO2 molecules (page 9 in the revised manuscript).
8. …CO2 required activation energy to adsorb onto… What's the meaning of activation energy? …such adsorption did not occur… Which is "such adsorption"?

Response
We thank the reviewer for this comment. Activation energy means CO2 molecules cannot freely enter the pore of PCP-3,5-pdc but has to overcome an energy barrier. After rechecking the caption of Supplementary Figure 13 (page S23), we removed the statement "The high-pressure gas sorption results and adsorption isotherms measured at low temperatures showed that CO2 required activation energy to adsorb onto PCP-3,5-pdc. But such adsorption did not occur with C2H4, C2H2." 9. Specify the pressure of isobars. Specify the phase used for computational simulations.

Response
We thank the reviewer for this comment. The pressure for the isobar measurement is 100 kPa. We have added this information to the revised Supplementary Information (page S2). Additionally, both the activated and open phases were used in the computational simulations, and we have added this statement to the Computational Details section in the revised Supplementary Information (page S6). 10. The volume of N2, CH4, and C2H4 adsorbed in the binary adsorption mixtures was negligible. They should not be claimed as negligible. If negligible, the uptakes should not be compared and calculated. … optimum selectivity… How optimum? This is a typical feature of gate-opening adsorption. What is "this"?

Response
We thank the reviewer for this comment.
We have revised the sentence "The volume of N2, CH4, and C2H4 adsorbed in the binary adsorption mixtures was negligible" to "The volume of N2, CH4, and C2H4 adsorbed in the binary adsorption mixtures was 0.5, 2.8 and 3.3 mL·g -1 , respectively" (page 11 in the revised manuscript).
Additionally, we have removed the word "optimum". In reference 39, we have shown that simultaneous adsorption of more than one gas molecule is necessary to overcome the deformation energy of PCP framework induced by gas adsorption, which is an important feature for gate-opening adsorption. Therefore, we have revised the sentence "Interestingly, the total BE value is the largest (the most negative) when one CO2 molecule is adsorbed at site I, two CO2 molecules are adsorbed at site IIA, and one CO2 molecule is adsorbed at one site IIB of two unit cells, which PCP•3.5CO2 represents. This is a typical feature of gate-opening adsorption." to "Interestingly, the total BE value is the largest (the most negative) when one CO2 molecule is adsorbed at site I, two CO2 molecules are adsorbed at site IIA, and one CO2 molecule is adsorbed at one site IIB of two unit cells, suggesting that simultaneous adsorption of more than one CO2 molecules can happen in PCP-3,5-pdc, which is a typical feature of gate-opening adsorption" (Page 15 in the revised manuscript).